Foreign Minister Faruq al-Shara told delegates at a meeting of Iraq's neighbours in Istanbul on Sunday that Damascus would "take the necessary legal steps to reopen relations as quickly as possible".
Ties between the two countries were severed in 1980 over Damascus's support for Tehran during the Iran-Iraq war.
Baghdad and the US authorities have accused Syria of allowing foreign fighters to cross the border to join the insurgency, charges denied by Damascus.
At the moment, each country has an interest section established in the other's capital.
Last year, the US imposed sanctions on Syrian President Bashar al-Asad's government, accusing it of helping resistance groups in Iraq and supporting terrorism.
At the Istanbul conference, Iraq's neighbours pledged on Saturday to boost border security and increase intelligence sharing with the country's newly elected government.
The neighbours also agreed to hold a meeting of their interior ministers in Turkey in the coming weeks to discuss details of how they could better monitor their borders.
Iraq's neighbours have pledged
to boost intelligence sharing
Iraq's neighbours have been deeply concerned that violence and ethnic instability in Iraq could spread throughout the region, and that danger was a major topic of discussion during the meeting, held at a former Ottoman palace overlooking the Bosphorus.
All of Iraq's neighbours except non-Arab Shia Iran are Sunni-controlled. Iran has said it wants an end to violence in its big western neighbour.
For its part, Iraq called on its neighbours to support its new government and help secure its borders to promote stability and keep the country together.
"We will hold them to their words. We expect more assistance. Our neighbours can help, can be more constructive," Foreign Minister Hushiar Zibari told reporters on the sidelines.
In their final communique, the neighbours "expressed their determination ... to increase their cooperation on the overall border security with Iraq ... including ... exchange of intelligence with Iraq with the primary aim of stemming terrorist and other illegal infiltrations to and from Iraq."
"We will hold them to their words. We expect more assistance"
Iraq Foreign Minister Hushyar Zibari
It was not clear what steps the neighbours could take.
Iraq's neighbours have pledged to boost border security and increase intelligence sharing with the country's newly elected government.
The meeting was the eighth such by the neighbours who "pledged to support and cooperate with the newly elected" government and stressed the unity and territorial integrity of Iraq.
Source of concern
Turkish Prime Minister Recep Tayyip Erdogan said as he opened the meeting: "Iraq cannot be a place where one entity prevails over the others, nor can it be a place divided up as desired."
Erdogan stressed that violence in Iraq was a source of concern to all neighbouring countries. "Such attempts will meet the reaction of the countries of the region and the international community," he said.
"It is very important that this meeting was held right after the formation of the Iraqi government because it is important for the protection of the whole region," Iranian Foreign Minister Kamal Kharazi said.
The next meeting would be held in the Iranian capital, Tehran.